If the angle between the line joining end point of minor of an ellipse

1.	If the angle between the line joining end point of minor of an ellipse with its foci π/2 then the hethe eccentricity of the ellipse is(A) 1/2(B) 1/√2(C)√3/2(D) 1/2√2
Answer» Equation of ellipse isx^2/a^2+y^2/b^2=1(a > b) Slope of BS=−b/ae=m1 Slope of BS'=b/ae=m2 Angle between BS and BS' is90° m1m2=−1 b^2=a^2e^2 a^2(1−e^2)=a^2e^2 b^2=a^2(1−e^2) 2e^2=1 e=1/√2

If the angle between the line joining end point of minor of an ellipse with its foci π/2 then the hethe eccentricity of the ellipse is(A) 1/2(B) 1/√2(C)√3/2(D) 1/2√2

Answer»

Equation of ellipse isx^2/a^2+y^2/b^2=1(a > b)

Slope of BS=−b/ae=m1

Slope of BS'=b/ae=m2

Angle between BS and BS' is90°

m1m2=−1

b^2=a^2e^2

a^2(1−e^2)=a^2e^2

b^2=a^2(1−e^2)

2e^2=1

e=1/√2